Figure REF  depicts the \(\mathrm {K}^+/\pi ^+\)  ratios as functions of \(\sqrt{s_{NN}}\) . Symbols refer to the experimental results, at energies ranging from 5 GeV to \(5.44\)  TeV [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}. The dotted curve shows the generic (non)extensive calculations, at partial–chemical nonequilibrium, i.e., varying \(\gamma _s\) , while \(\gamma _q=1\) . The solid curve illustrates the results, at full–chemical nonequilibrium, i.e., varying \(\gamma _s\)  and \(\gamma _q\) . The double–dashed curve gives the extensive BG calculations, at partial–chemical nonequilibrium [10]}, while the dashed curve presents the extensive BG calculations, at full–chemical nonequilibrium [11]}. The incapability of the equilibrium HRG model, i.e., \(\gamma _q=\gamma _s=1\) , in reproducing both the horn–structure of the \(\mathrm {K}^+/\pi ^+\)  ratios, at AGS, SPS, and low RHIC energies, and their measurements, at RHIC and LHC energies, is shown by the long–dashed curve.
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